"Moving cars is more important than moving people" is dumb policy which applies in basically every American city, but in addition to that my take is that a lot of "moving cars" policies actually don't help move cars at all. Anything which encourages a lot of lane switching in times of heavy traffic probably slows down traffic quite a bit. Sometimes rules are actually better than chaos.
If cars are the priority (they shouldn't be, but obviously they are), run an experiment. Measure numbers/speed without shunting them into the bus lane, and do the same when you do. The results might be surprising. Or not!